As remarked above, the random initialization of parameters endows \(\mathsf {GAP}_n\)  with a translation-invariant prior, which may be well-suited to many image-classification tasks. This observation, combined with the result from thm:change of prior that the function space of \(\mathsf {GAP}_n\)  is the smallest, suggests that networks with this architecture may enjoy favorable generalization properties. Indeed, prior work [1]}, [2]}, [3]} has found that \(\mathsf {GAP}_n\)  can significantly outperform \(\mathsf {VEC}_n\) , \(\mathsf {LCN}_n\) , and \({\mathsf {FCN}}_n\) , a conclusion we also find in Sec. .
